Question

Find the derivative of the function by the limit process.

f(x)=1/sqrt(x)

I've worked through my problem and got f'(x) to be -1/2x but the actual answer is -1/2x^3/2? Where did the 3/2 power come from?
Any help is greatly appreciated!

Answer 1

f(x+h)-f(x) = 1/√(x+h) - 1/√x
= (√x - √(x+h))/√(x(x+h))
= (x-(x+h))/(√x(x+h))(√x+√(x+h))
= -h/(√x(x+h))(√x+√(x+h))
divide by h and you have

-1/(√x(x+h))(√x+√(x+h))
as h->0, that is
-1/(√x^2 (2√x))
= -1/(x*2√x)

I suspect a √ got lost somewhere in the shuffle. Should have shown your work. I might have picked it up more easily than doing it myself...